Finite Group Databasebeta

← Group #10693073

Character table — Group #10693073

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size111122222222222222224444444444488888888888888888888888888161616161616242424242424242448484848
order12222234444446661212121244466121212121212444488881212121212121212121224242424242424248824242424244488884488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ411111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ51111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1
χ61111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111
χ81111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1
χ91111111-1-1-1-1-1-1111-1-1-1-111-111-1-111-1-111-1-1ii−i−i1-11111-1-1-1-1iiii−i−i−i−ii−iii−i−i11-1-1ii−i−i1-1i−i
χ101111111-1-1-1-1-1-1111-1-1-1-111-111-1-111-1-111-1-1ii−i−i1-11111-1-1-1-1iiii−i−i−i−ii−iii−i−i-1-111−i−iii-11−ii
χ111111111-1-1-1-1-1-1111-1-1-1-111-111-1-111-1-111-1-1−i−iii1-11111-1-1-1-1−i−i−i−iiiii−ii−i−iii11-1-1−i−iii1-1−ii
χ121111111-1-1-1-1-1-1111-1-1-1-111-111-1-111-1-111-1-1−i−iii1-11111-1-1-1-1−i−i−i−iiiii−ii−i−iii-1-111ii−i−i-11i−i
χ131111111-1-1-1-1-1-1111-1-1-1-111-111-1-111-1-1-1-111ii−i−i1-1-1-1-1-11111iiii−i−i−i−i−ii−i−iii11-1-1ii−i−i-11−ii
χ141111111-1-1-1-1-1-1111-1-1-1-111-111-1-111-1-1-1-111ii−i−i1-1-1-1-1-11111iiii−i−i−i−i−ii−i−iii-1-111−i−iii1-1i−i
χ151111111-1-1-1-1-1-1111-1-1-1-111-111-1-111-1-1-1-111−i−iii1-1-1-1-1-11111−i−i−i−iiiiii−iii−i−i11-1-1−i−iii-11i−i
χ161111111-1-1-1-1-1-1111-1-1-1-111-111-1-111-1-1-1-111−i−iii1-1-1-1-1-11111−i−i−i−iiiiii−iii−i−i-1-111ii−i−i1-1−ii
χ1722222222222-2-22222222-2-2-22222-2-2-2-200000000-2-200000000000000000000002-22-200000000
χ1822222222222-2-22222222-2-2-22222-2-2-2-200000000-2-20000000000000000000000-22-2200000000
χ192222222-2-2-2-222222-2-2-2-2-2-2222-2-2-2-22200000000-2200000000000000000000002-2-2200000000
χ202222222-2-2-2-222222-2-2-2-2-2-2222-2-2-2-22200000000-220000000000000000000000-222-200000000
χ21222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1000000000000
χ22222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111-2-21111000000000000
χ23222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-1-2-21111000000000000
χ24222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1111111111111111122-1-1-1-1000000000000
χ25222222-1-2-2-2-2-2-2-1-1-1111122-2-1-111-1-11122-2-22i2i−2i−2i-11-1-1-1-11111−i−i−i−iiiii2i−2i−i−iii000000000000
χ26222222-1-2-2-2-2-2-2-1-1-1111122-2-1-111-1-11122-2-2−2i−2i2i2i-11-1-1-1-11111iiii−i−i−i−i−2i2iii−i−i000000000000
χ27222222-1-2-2-2-2-2-2-1-1-1111122-2-1-111-1-111-2-2222i2i−2i−2i-111111-1-1-1-1−i−i−i−iiiii−2i2iii−i−i000000000000
χ28222222-1-2-2-2-2-2-2-1-1-1111122-2-1-111-1-111-2-222−2i−2i2i2i-111111-1-1-1-1iiii−i−i−i−i2i−2i−i−iii000000000000
χ292222-2-2222-2-22222222222-2-2-2-2-2-2222200002-22-2-2-20000000022-2-222-2-2000000000000000000
χ302222-2-2222-2-22222222222-2-2-2-2-2-222220000-22-22-2-200000000-2-222-2-222000000000000000000
χ312222-2-2222-2-2-2-22222222-222-2-2-2-2-2-2-2-20000000022000000000000000000000000002i−2i2i−2i0000
χ322222-2-2222-2-2-2-22222222-222-2-2-2-2-2-2-2-2000000002200000000000000000000000000−2i2i−2i2i0000
χ332222-2-22-2-22222222-2-2-2-2-22-2-2-222-2-222000000002-2000000000000000000000000002-2-220000
χ342222-2-22-2-22222222-2-2-2-2-22-2-2-222-2-222000000002-200000000000000000000000000-222-20000
χ352222-2-22-2-222-2-2222-2-2-2-22-22-2-22222-2-200002i−2i−2i2i-22000000002i2i−2i−2i−2i−2i2i2i000000000000000000
χ362222-2-22-2-222-2-2222-2-2-2-22-22-2-22222-2-20000−2i2i2i−2i-2200000000−2i−2i2i2i2i2i−2i−2i000000000000000000
χ372222-2-2-122-2-222-1-1-1-1-1-1-12-2-21111-1-1-1-100002-22-211−i3−i3i3i3−i3−i3i3i3-1-111-1-11100−i3i3−i3i3000000000000
χ382222-2-2-122-2-222-1-1-1-1-1-1-12-2-21111-1-1-1-100002-22-211i3i3−i3−i3i3i3−i3−i3-1-111-1-11100i3−i3i3−i3000000000000
χ392222-2-2-122-2-222-1-1-1-1-1-1-12-2-21111-1-1-1-10000-22-2211−i3−i3i3i3−i3−i3i3i311-1-111-1-100i3−i3i3−i3000000000000
χ402222-2-2-122-2-222-1-1-1-1-1-1-12-2-21111-1-1-1-10000-22-2211i3i3−i3−i3i3i3−i3−i311-1-111-1-100−i3i3−i3i3000000000000
χ412222-2-2-1-2-222-2-2-1-1-111112-2211-1-1-1-11100002i−2i−2i2i1-1−i3−i3i3i3i3i3−i3−i3−i−iiiii−i−i003−3−33000000000000
χ422222-2-2-1-2-222-2-2-1-1-111112-2211-1-1-1-11100002i−2i−2i2i1-1i3i3−i3−i3−i3−i3i3i3−i−iiiii−i−i00−333−3000000000000
χ432222-2-2-1-2-222-2-2-1-1-111112-2211-1-1-1-1110000−2i2i2i−2i1-1−i3−i3i3i3i3i3−i3−i3ii−i−i−i−iii00−333−3000000000000
χ442222-2-2-1-2-222-2-2-1-1-111112-2211-1-1-1-1110000−2i2i2i−2i1-1i3i3−i3−i3−i3−i3i3i3ii−i−i−i−iii003−3−33000000000000
χ45444444-24444-4-4-2-2-2-2-2-2-2-4-4-4-2-2-2-2222200000000220000000000000000000000000000000000
χ46444444-2-4-4-4-444-2-2-22222-4-44-2-22222-2-2000000002-20000000000000000000000000000000000
χ474444-4-4-244-4-4-4-4-2-2-2-2-2-2-2-4442222222200000000-2-20000000000000000000000000000000000
χ484444-4-4-2-4-44444-2-2-22222-44-422-2-222-2-200000000-220000000000000000000000000000000000
χ494-44-400400004i−4i-44-400000000000004i−4i2-22i−2i0000002-22-22i−2i2i−2i00000000000000000000000000
χ504-44-400400004i−4i-44-400000000000004i−4i-22−2i2i000000-22-22−2i2i−2i2i00000000000000000000000000
χ514-44-40040000−4i4i-44-40000000000000−4i4i2-2−2i2i0000002-22-2−2i2i−2i2i00000000000000000000000000
χ524-44-40040000−4i4i-44-40000000000000−4i4i-222i−2i000000-22-222i−2i2i−2i00000000000000000000000000
χ534-44-400-200004i−4i2-222323−23−230000000−2i32i3−2i2i2-22i−2i000000−1−i31+i3−1+i31−i32ζ11−2ζ112ζ7−2ζ700000000000000000000000000
χ544-44-400-200004i−4i2-222323−23−230000000−2i32i3−2i2i-22−2i2i0000001+i3−1−i31−i3−1+i3−2ζ112ζ11−2ζ72ζ700000000000000000000000000
χ554-44-400-200004i−4i2-22−23−23232300000002i3−2i3−2i2i2-22i−2i000000−1+i31−i3−1−i31+i32ζ7−2ζ72ζ11−2ζ1100000000000000000000000000
χ564-44-400-200004i−4i2-22−23−23232300000002i3−2i3−2i2i-22−2i2i0000001−i3−1+i31+i3−1−i3−2ζ72ζ7−2ζ112ζ1100000000000000000000000000
χ574-44-400-20000−4i4i2-222323−23−2300000002i3−2i32i−2i2-2−2i2i000000−1+i31−i3−1−i31+i3−2ζ72ζ7−2ζ112ζ1100000000000000000000000000
χ584-44-400-20000−4i4i2-222323−23−2300000002i3−2i32i−2i-222i−2i0000001−i3−1+i31+i3−1−i32ζ7−2ζ72ζ11−2ζ1100000000000000000000000000
χ594-44-400-20000−4i4i2-22−23−2323230000000−2i32i32i−2i2-2−2i2i000000−1−i31+i3−1+i31−i3−2ζ112ζ11−2ζ72ζ700000000000000000000000000
χ604-44-400-20000−4i4i2-22−23−2323230000000−2i32i32i−2i-222i−2i0000001+i3−1−i31−i3−1+i32ζ11−2ζ112ζ7−2ζ700000000000000000000000000
χ614-4-444-444i−4i4i−4i00-4-444i−4i4i−4i0004-44i−4i000000000000000000000000000000000000000000000000
χ624-4-444-44−4i4i−4i4i00-4-44−4i4i−4i4i0004-4−4i4i000000000000000000000000000000000000000000000000
χ634-4-444-4-24i−4i4i−4i0022-2−2i2i−2i2i000-22−2i2i0000000000000000000000−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11000000000000000000
χ644-4-444-4-24i−4i4i−4i0022-2−2i2i−2i2i000-22−2i2i0000000000000000000000ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11000000000000000000
χ654-4-444-4-2−4i4i−4i4i0022-22i−2i2i−2i000-222i−2i0000000000000000000000−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11000000000000000000
χ664-4-444-4-2−4i4i−4i4i0022-22i−2i2i−2i000-222i−2i0000000000000000000000ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11000000000000000000
χ674-4-44-4444i−4i−4i4i00-4-444i−4i4i−4i000-44−4i4i000000000000000000000000000000000000000000000000
χ684-4-44-444−4i4i4i−4i00-4-44−4i4i−4i4i000-444i−4i000000000000000000000000000000000000000000000000
χ694-4-44-44-24i−4i−4i4i0022-2−2i2i−2i2i0002-22i−2i0000000000000000000000−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11000000000000000000
χ704-4-44-44-24i−4i−4i4i0022-2−2i2i−2i2i0002-22i−2i0000000000000000000000ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11000000000000000000
χ714-4-44-44-2−4i4i4i−4i0022-22i−2i2i−2i0002-2−2i2i0000000000000000000000−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11000000000000000000
χ724-4-44-44-2−4i4i4i−4i0022-22i−2i2i−2i0002-2−2i2i0000000000000000000000ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11000000000000000000
χ7388-8-80080000008-8-800000000000000000000000000000000000000000000000000000000000
χ7488-8-800-4000000-444−4i34i34i3−4i30000000000000000000000000000000000000000000000000000000
χ7588-8-800-4000000-4444i3−4i3−4i34i30000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.